Multispin magnons on deformed $ AdS_{3}\times S^{3} $

In this paper, using the holographic prescription, we study multispin bound states and their dispersion relations over the $\kappa$-deformed $AdS_{3}\times S^{3}$ background. In the first part of our analysis, considering the conformal gauge conditions (associated with the Polyakov action) we explore the dispersion relation associated with spin two bound states at strong coupling. We solve corresponding world-sheet fluctuations and compute all the conserved quantities associated with the stringy dynamics over the deformed background. In the second part of our analysis, we perform similar analysis for spin three configurations. In both cases, we observe the emergence of non trivial background deformation that vanishes in the limit, $\kappa \rightarrow 0$.